Modeling methodology for nonlinear physiological systems

A general modeling approach for a broad class of nonlinear systems is presented that uses the concept of principal dynamic modes (PDMs). These PDMs constitute a filter bank whose outputs feed into a multi-input static nonlinearity of multinomial (polynomial) form to yield a general model for the broad class of Volterra systems. Because the practically obtainable models (from stimulus-response data) are of arbitrary order of nonlinearity, this approach is applicable to many nonlinear physiological systems heretofore beyond our methodological means. Two specific methods are proposed for the estimation of these PDMs and the associated nonlinearities from stimulus-response data. Method I uses eigendecomposition of a properly constructed matrix using the first two kernel estimates (obtained by existing methods). Method II uses a particular class of feedforward artificial neural networks with polynomial activation functions. The efficacy of these two methods is demonstrated with computer-simulated examples, and their relative performance is discussed. The advent of this approach promises a practicable solution to the vexing problem of modeling highly nonlinear physiological systems, provided that experimental data be available for reliable estimation of the requisite PDMs.